/*-
 * Copyright 2002 Niels Provos <provos@citi.umich.edu>
 * All rights reserved.
 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions
 * are met:
 * 1. Redistributions of source code must retain the above copyright
 *    notice, this list of conditions and the following disclaimer.
 * 2. Redistributions in binary form must reproduce the above copyright
 *    notice, this list of conditions and the following disclaimer in the
 *    documentation and/or other materials provided with the distribution.
 *
 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
 * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
 * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
 * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
 * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
 * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
 * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
 * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
 * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
 * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
 */

#ifndef UV_TREE_H_
#define UV_TREE_H_

#ifndef UV__UNUSED
#if __GNUC__
#define UV__UNUSED __attribute__((unused))
#else
#define UV__UNUSED
#endif
#endif

/*
 * This file defines data structures for different types of trees:
 * splay trees and red-black trees.
 *
 * A splay tree is a self-organizing data structure.  Every operation
 * on the tree causes a splay to happen.  The splay moves the requested
 * node to the root of the tree and partly rebalances it.
 *
 * This has the benefit that request locality causes faster lookups as
 * the requested nodes move to the top of the tree.  On the other hand,
 * every lookup causes memory writes.
 *
 * The Balance Theorem bounds the total access time for m operations
 * and n inserts on an initially empty tree as O((m + n)lg n).  The
 * amortized cost for a sequence of m accesses to a splay tree is O(lg n);
 *
 * A red-black tree is a binary search tree with the node color as an
 * extra attribute.  It fulfills a set of conditions:
 *  - every search path from the root to a leaf consists of the
 *    same number of black nodes,
 *  - each red node (except for the root) has a black parent,
 *  - each leaf node is black.
 *
 * Every operation on a red-black tree is bounded as O(lg n).
 * The maximum height of a red-black tree is 2lg (n+1).
 */

#define SPLAY_HEAD(name, type)                        \
    struct name {                                     \
        struct type* sph_root; /* root of the tree */ \
    }

#define SPLAY_INITIALIZER(root) \
    {                           \
        NULL                    \
    }

#define SPLAY_INIT(root)         \
    do {                         \
        (root)->sph_root = NULL; \
    } while (/*CONSTCOND*/ 0)

#define SPLAY_ENTRY(type)                           \
    struct {                                        \
        struct type* spe_left; /* left element */   \
        struct type* spe_right; /* right element */ \
    }

#define SPLAY_LEFT(elm, field) (elm)->field.spe_left
#define SPLAY_RIGHT(elm, field) (elm)->field.spe_right
#define SPLAY_ROOT(head) (head)->sph_root
#define SPLAY_EMPTY(head) (SPLAY_ROOT(head) == NULL)

/* SPLAY_ROTATE_{LEFT,RIGHT} expect that tmp hold SPLAY_{RIGHT,LEFT} */
#define SPLAY_ROTATE_RIGHT(head, tmp, field)                           \
    do {                                                               \
        SPLAY_LEFT((head)->sph_root, field) = SPLAY_RIGHT(tmp, field); \
        SPLAY_RIGHT(tmp, field) = (head)->sph_root;                    \
        (head)->sph_root = tmp;                                        \
    } while (/*CONSTCOND*/ 0)

#define SPLAY_ROTATE_LEFT(head, tmp, field)                            \
    do {                                                               \
        SPLAY_RIGHT((head)->sph_root, field) = SPLAY_LEFT(tmp, field); \
        SPLAY_LEFT(tmp, field) = (head)->sph_root;                     \
        (head)->sph_root = tmp;                                        \
    } while (/*CONSTCOND*/ 0)

#define SPLAY_LINKLEFT(head, tmp, field)                        \
    do {                                                        \
        SPLAY_LEFT(tmp, field) = (head)->sph_root;              \
        tmp = (head)->sph_root;                                 \
        (head)->sph_root = SPLAY_LEFT((head)->sph_root, field); \
    } while (/*CONSTCOND*/ 0)

#define SPLAY_LINKRIGHT(head, tmp, field)                        \
    do {                                                         \
        SPLAY_RIGHT(tmp, field) = (head)->sph_root;              \
        tmp = (head)->sph_root;                                  \
        (head)->sph_root = SPLAY_RIGHT((head)->sph_root, field); \
    } while (/*CONSTCOND*/ 0)

#define SPLAY_ASSEMBLE(head, node, left, right, field)                   \
    do {                                                                 \
        SPLAY_RIGHT(left, field) = SPLAY_LEFT((head)->sph_root, field);  \
        SPLAY_LEFT(right, field) = SPLAY_RIGHT((head)->sph_root, field); \
        SPLAY_LEFT((head)->sph_root, field) = SPLAY_RIGHT(node, field);  \
        SPLAY_RIGHT((head)->sph_root, field) = SPLAY_LEFT(node, field);  \
    } while (/*CONSTCOND*/ 0)

/* Generates prototypes and inline functions */

#define SPLAY_PROTOTYPE(name, type, field, cmp)                   \
    void name##_SPLAY(struct name*, struct type*);                \
    void name##_SPLAY_MINMAX(struct name*, int);                  \
    struct type* name##_SPLAY_INSERT(struct name*, struct type*); \
    struct type* name##_SPLAY_REMOVE(struct name*, struct type*); \
                                                                  \
    /* Finds the node with the same key as elm */                 \
    static __inline struct type*                                  \
        name##_SPLAY_FIND(struct name* head, struct type* elm)    \
    {                                                             \
        if (SPLAY_EMPTY(head))                                    \
            return (NULL);                                        \
        name##_SPLAY(head, elm);                                  \
        if ((cmp)(elm, (head)->sph_root) == 0)                    \
            return (head->sph_root);                              \
        return (NULL);                                            \
    }                                                             \
                                                                  \
    static __inline struct type*                                  \
        name##_SPLAY_NEXT(struct name* head, struct type* elm)    \
    {                                                             \
        name##_SPLAY(head, elm);                                  \
        if (SPLAY_RIGHT(elm, field) != NULL) {                    \
            elm = SPLAY_RIGHT(elm, field);                        \
            while (SPLAY_LEFT(elm, field) != NULL) {              \
                elm = SPLAY_LEFT(elm, field);                     \
            }                                                     \
        } else                                                    \
            elm = NULL;                                           \
        return (elm);                                             \
    }                                                             \
                                                                  \
    static __inline struct type*                                  \
        name##_SPLAY_MIN_MAX(struct name* head, int val)          \
    {                                                             \
        name##_SPLAY_MINMAX(head, val);                           \
        return (SPLAY_ROOT(head));                                \
    }

/* Main splay operation.
 * Moves node close to the key of elm to top
 */
#define SPLAY_GENERATE(name, type, field, cmp)                                  \
    struct type*                                                                \
        name##_SPLAY_INSERT(struct name* head, struct type* elm)                \
    {                                                                           \
        if (SPLAY_EMPTY(head)) {                                                \
            SPLAY_LEFT(elm, field) = SPLAY_RIGHT(elm, field) = NULL;            \
        } else {                                                                \
            int __comp;                                                         \
            name##_SPLAY(head, elm);                                            \
            __comp = (cmp)(elm, (head)->sph_root);                              \
            if (__comp < 0) {                                                   \
                SPLAY_LEFT(elm, field) = SPLAY_LEFT((head)->sph_root, field);   \
                SPLAY_RIGHT(elm, field) = (head)->sph_root;                     \
                SPLAY_LEFT((head)->sph_root, field) = NULL;                     \
            } else if (__comp > 0) {                                            \
                SPLAY_RIGHT(elm, field) = SPLAY_RIGHT((head)->sph_root, field); \
                SPLAY_LEFT(elm, field) = (head)->sph_root;                      \
                SPLAY_RIGHT((head)->sph_root, field) = NULL;                    \
            } else                                                              \
                return ((head)->sph_root);                                      \
        }                                                                       \
        (head)->sph_root = (elm);                                               \
        return (NULL);                                                          \
    }                                                                           \
                                                                                \
    struct type*                                                                \
        name##_SPLAY_REMOVE(struct name* head, struct type* elm)                \
    {                                                                           \
        struct type* __tmp;                                                     \
        if (SPLAY_EMPTY(head))                                                  \
            return (NULL);                                                      \
        name##_SPLAY(head, elm);                                                \
        if ((cmp)(elm, (head)->sph_root) == 0) {                                \
            if (SPLAY_LEFT((head)->sph_root, field) == NULL) {                  \
                (head)->sph_root = SPLAY_RIGHT((head)->sph_root, field);        \
            } else {                                                            \
                __tmp = SPLAY_RIGHT((head)->sph_root, field);                   \
                (head)->sph_root = SPLAY_LEFT((head)->sph_root, field);         \
                name##_SPLAY(head, elm);                                        \
                SPLAY_RIGHT((head)->sph_root, field) = __tmp;                   \
            }                                                                   \
            return (elm);                                                       \
        }                                                                       \
        return (NULL);                                                          \
    }                                                                           \
                                                                                \
    void                                                                        \
        name##_SPLAY(struct name* head, struct type* elm)                       \
    {                                                                           \
        struct type __node, *__left, *__right, *__tmp;                          \
        int __comp;                                                             \
                                                                                \
        SPLAY_LEFT(&__node, field) = SPLAY_RIGHT(&__node, field) = NULL;        \
        __left = __right = &__node;                                             \
                                                                                \
        while ((__comp = (cmp)(elm, (head)->sph_root)) != 0) {                  \
            if (__comp < 0) {                                                   \
                __tmp = SPLAY_LEFT((head)->sph_root, field);                    \
                if (__tmp == NULL)                                              \
                    break;                                                      \
                if ((cmp)(elm, __tmp) < 0) {                                    \
                    SPLAY_ROTATE_RIGHT(head, __tmp, field);                     \
                    if (SPLAY_LEFT((head)->sph_root, field) == NULL)            \
                        break;                                                  \
                }                                                               \
                SPLAY_LINKLEFT(head, __right, field);                           \
            } else if (__comp > 0) {                                            \
                __tmp = SPLAY_RIGHT((head)->sph_root, field);                   \
                if (__tmp == NULL)                                              \
                    break;                                                      \
                if ((cmp)(elm, __tmp) > 0) {                                    \
                    SPLAY_ROTATE_LEFT(head, __tmp, field);                      \
                    if (SPLAY_RIGHT((head)->sph_root, field) == NULL)           \
                        break;                                                  \
                }                                                               \
                SPLAY_LINKRIGHT(head, __left, field);                           \
            }                                                                   \
        }                                                                       \
        SPLAY_ASSEMBLE(head, &__node, __left, __right, field);                  \
    }                                                                           \
                                                                                \
    /* Splay with either the minimum or the maximum element                     \
     * Used to find minimum or maximum element in tree.                         \
     */                                                                         \
    void name##_SPLAY_MINMAX(struct name* head, int __comp)                     \
    {                                                                           \
        struct type __node, *__left, *__right, *__tmp;                          \
                                                                                \
        SPLAY_LEFT(&__node, field) = SPLAY_RIGHT(&__node, field) = NULL;        \
        __left = __right = &__node;                                             \
                                                                                \
        while (1) {                                                             \
            if (__comp < 0) {                                                   \
                __tmp = SPLAY_LEFT((head)->sph_root, field);                    \
                if (__tmp == NULL)                                              \
                    break;                                                      \
                if (__comp < 0) {                                               \
                    SPLAY_ROTATE_RIGHT(head, __tmp, field);                     \
                    if (SPLAY_LEFT((head)->sph_root, field) == NULL)            \
                        break;                                                  \
                }                                                               \
                SPLAY_LINKLEFT(head, __right, field);                           \
            } else if (__comp > 0) {                                            \
                __tmp = SPLAY_RIGHT((head)->sph_root, field);                   \
                if (__tmp == NULL)                                              \
                    break;                                                      \
                if (__comp > 0) {                                               \
                    SPLAY_ROTATE_LEFT(head, __tmp, field);                      \
                    if (SPLAY_RIGHT((head)->sph_root, field) == NULL)           \
                        break;                                                  \
                }                                                               \
                SPLAY_LINKRIGHT(head, __left, field);                           \
            }                                                                   \
        }                                                                       \
        SPLAY_ASSEMBLE(head, &__node, __left, __right, field);                  \
    }

#define SPLAY_NEGINF -1
#define SPLAY_INF 1

#define SPLAY_INSERT(name, x, y) name##_SPLAY_INSERT(x, y)
#define SPLAY_REMOVE(name, x, y) name##_SPLAY_REMOVE(x, y)
#define SPLAY_FIND(name, x, y) name##_SPLAY_FIND(x, y)
#define SPLAY_NEXT(name, x, y) name##_SPLAY_NEXT(x, y)
#define SPLAY_MIN(name, x) (SPLAY_EMPTY(x) ? NULL \
                                           : name##_SPLAY_MIN_MAX(x, SPLAY_NEGINF))
#define SPLAY_MAX(name, x) (SPLAY_EMPTY(x) ? NULL \
                                           : name##_SPLAY_MIN_MAX(x, SPLAY_INF))

#define SPLAY_FOREACH(x, name, head)  \
    for ((x) = SPLAY_MIN(name, head); \
         (x) != NULL;                 \
         (x) = SPLAY_NEXT(name, head, x))

/* Macros that define a red-black tree */
#define RB_HEAD(name, type)                           \
    struct name {                                     \
        struct type* rbh_root; /* root of the tree */ \
    }

#define RB_INITIALIZER(root) \
    {                        \
        NULL                 \
    }

#define RB_INIT(root)            \
    do {                         \
        (root)->rbh_root = NULL; \
    } while (/*CONSTCOND*/ 0)

#define RB_BLACK 0
#define RB_RED 1
#define RB_ENTRY(type)                                \
    struct {                                          \
        struct type* rbe_left; /* left element */     \
        struct type* rbe_right; /* right element */   \
        struct type* rbe_parent; /* parent element */ \
        int rbe_color; /* node color */               \
    }

#define RB_LEFT(elm, field) (elm)->field.rbe_left
#define RB_RIGHT(elm, field) (elm)->field.rbe_right
#define RB_PARENT(elm, field) (elm)->field.rbe_parent
#define RB_COLOR(elm, field) (elm)->field.rbe_color
#define RB_ROOT(head) (head)->rbh_root
#define RB_EMPTY(head) (RB_ROOT(head) == NULL)

#define RB_SET(elm, parent, field)                         \
    do {                                                   \
        RB_PARENT(elm, field) = parent;                    \
        RB_LEFT(elm, field) = RB_RIGHT(elm, field) = NULL; \
        RB_COLOR(elm, field) = RB_RED;                     \
    } while (/*CONSTCOND*/ 0)

#define RB_SET_BLACKRED(black, red, field) \
    do {                                   \
        RB_COLOR(black, field) = RB_BLACK; \
        RB_COLOR(red, field) = RB_RED;     \
    } while (/*CONSTCOND*/ 0)

#ifndef RB_AUGMENT
#define RB_AUGMENT(x) \
    do {              \
    } while (0)
#endif

#define RB_ROTATE_LEFT(head, elm, tmp, field)                          \
    do {                                                               \
        (tmp) = RB_RIGHT(elm, field);                                  \
        if ((RB_RIGHT(elm, field) = RB_LEFT(tmp, field)) != NULL) {    \
            RB_PARENT(RB_LEFT(tmp, field), field) = (elm);             \
        }                                                              \
        RB_AUGMENT(elm);                                               \
        if ((RB_PARENT(tmp, field) = RB_PARENT(elm, field)) != NULL) { \
            if ((elm) == RB_LEFT(RB_PARENT(elm, field), field))        \
                RB_LEFT(RB_PARENT(elm, field), field) = (tmp);         \
            else                                                       \
                RB_RIGHT(RB_PARENT(elm, field), field) = (tmp);        \
        } else                                                         \
            (head)->rbh_root = (tmp);                                  \
        RB_LEFT(tmp, field) = (elm);                                   \
        RB_PARENT(elm, field) = (tmp);                                 \
        RB_AUGMENT(tmp);                                               \
        if ((RB_PARENT(tmp, field)))                                   \
            RB_AUGMENT(RB_PARENT(tmp, field));                         \
    } while (/*CONSTCOND*/ 0)

#define RB_ROTATE_RIGHT(head, elm, tmp, field)                         \
    do {                                                               \
        (tmp) = RB_LEFT(elm, field);                                   \
        if ((RB_LEFT(elm, field) = RB_RIGHT(tmp, field)) != NULL) {    \
            RB_PARENT(RB_RIGHT(tmp, field), field) = (elm);            \
        }                                                              \
        RB_AUGMENT(elm);                                               \
        if ((RB_PARENT(tmp, field) = RB_PARENT(elm, field)) != NULL) { \
            if ((elm) == RB_LEFT(RB_PARENT(elm, field), field))        \
                RB_LEFT(RB_PARENT(elm, field), field) = (tmp);         \
            else                                                       \
                RB_RIGHT(RB_PARENT(elm, field), field) = (tmp);        \
        } else                                                         \
            (head)->rbh_root = (tmp);                                  \
        RB_RIGHT(tmp, field) = (elm);                                  \
        RB_PARENT(elm, field) = (tmp);                                 \
        RB_AUGMENT(tmp);                                               \
        if ((RB_PARENT(tmp, field)))                                   \
            RB_AUGMENT(RB_PARENT(tmp, field));                         \
    } while (/*CONSTCOND*/ 0)

/* Generates prototypes and inline functions */
#define RB_PROTOTYPE(name, type, field, cmp) \
    RB_PROTOTYPE_INTERNAL(name, type, field, cmp, )
#define RB_PROTOTYPE_STATIC(name, type, field, cmp) \
    RB_PROTOTYPE_INTERNAL(name, type, field, cmp, UV__UNUSED static)
#define RB_PROTOTYPE_INTERNAL(name, type, field, cmp, attr)                     \
    attr void name##_RB_INSERT_COLOR(struct name*, struct type*);               \
    attr void name##_RB_REMOVE_COLOR(struct name*, struct type*, struct type*); \
    attr struct type* name##_RB_REMOVE(struct name*, struct type*);             \
    attr struct type* name##_RB_INSERT(struct name*, struct type*);             \
    attr struct type* name##_RB_FIND(struct name*, struct type*);               \
    attr struct type* name##_RB_NFIND(struct name*, struct type*);              \
    attr struct type* name##_RB_NEXT(struct type*);                             \
    attr struct type* name##_RB_PREV(struct type*);                             \
    attr struct type* name##_RB_MINMAX(struct name*, int);

/* Main rb operation.
 * Moves node close to the key of elm to top
 */
#define RB_GENERATE(name, type, field, cmp) \
    RB_GENERATE_INTERNAL(name, type, field, cmp, )
#define RB_GENERATE_STATIC(name, type, field, cmp) \
    RB_GENERATE_INTERNAL(name, type, field, cmp, UV__UNUSED static)
#define RB_GENERATE_INTERNAL(name, type, field, cmp, attr)                                                                                                                                      \
    attr void                                                                                                                                                                                   \
        name##_RB_INSERT_COLOR(struct name* head, struct type* elm)                                                                                                                             \
    {                                                                                                                                                                                           \
        struct type *parent, *gparent, *tmp;                                                                                                                                                    \
        while ((parent = RB_PARENT(elm, field)) != NULL && RB_COLOR(parent, field) == RB_RED) {                                                                                                 \
            gparent = RB_PARENT(parent, field);                                                                                                                                                 \
            if (parent == RB_LEFT(gparent, field)) {                                                                                                                                            \
                tmp = RB_RIGHT(gparent, field);                                                                                                                                                 \
                if (tmp && RB_COLOR(tmp, field) == RB_RED) {                                                                                                                                    \
                    RB_COLOR(tmp, field) = RB_BLACK;                                                                                                                                            \
                    RB_SET_BLACKRED(parent, gparent, field);                                                                                                                                    \
                    elm = gparent;                                                                                                                                                              \
                    continue;                                                                                                                                                                   \
                }                                                                                                                                                                               \
                if (RB_RIGHT(parent, field) == elm) {                                                                                                                                           \
                    RB_ROTATE_LEFT(head, parent, tmp, field);                                                                                                                                   \
                    tmp = parent;                                                                                                                                                               \
                    parent = elm;                                                                                                                                                               \
                    elm = tmp;                                                                                                                                                                  \
                }                                                                                                                                                                               \
                RB_SET_BLACKRED(parent, gparent, field);                                                                                                                                        \
                RB_ROTATE_RIGHT(head, gparent, tmp, field);                                                                                                                                     \
            } else {                                                                                                                                                                            \
                tmp = RB_LEFT(gparent, field);                                                                                                                                                  \
                if (tmp && RB_COLOR(tmp, field) == RB_RED) {                                                                                                                                    \
                    RB_COLOR(tmp, field) = RB_BLACK;                                                                                                                                            \
                    RB_SET_BLACKRED(parent, gparent, field);                                                                                                                                    \
                    elm = gparent;                                                                                                                                                              \
                    continue;                                                                                                                                                                   \
                }                                                                                                                                                                               \
                if (RB_LEFT(parent, field) == elm) {                                                                                                                                            \
                    RB_ROTATE_RIGHT(head, parent, tmp, field);                                                                                                                                  \
                    tmp = parent;                                                                                                                                                               \
                    parent = elm;                                                                                                                                                               \
                    elm = tmp;                                                                                                                                                                  \
                }                                                                                                                                                                               \
                RB_SET_BLACKRED(parent, gparent, field);                                                                                                                                        \
                RB_ROTATE_LEFT(head, gparent, tmp, field);                                                                                                                                      \
            }                                                                                                                                                                                   \
        }                                                                                                                                                                                       \
        RB_COLOR(head->rbh_root, field) = RB_BLACK;                                                                                                                                             \
    }                                                                                                                                                                                           \
                                                                                                                                                                                                \
    attr void                                                                                                                                                                                   \
        name##_RB_REMOVE_COLOR(struct name* head, struct type* parent,                                                                                                                          \
            struct type* elm)                                                                                                                                                                   \
    {                                                                                                                                                                                           \
        struct type* tmp;                                                                                                                                                                       \
        while ((elm == NULL || RB_COLOR(elm, field) == RB_BLACK) && elm != RB_ROOT(head)) {                                                                                                     \
            if (RB_LEFT(parent, field) == elm) {                                                                                                                                                \
                tmp = RB_RIGHT(parent, field);                                                                                                                                                  \
                if (RB_COLOR(tmp, field) == RB_RED) {                                                                                                                                           \
                    RB_SET_BLACKRED(tmp, parent, field);                                                                                                                                        \
                    RB_ROTATE_LEFT(head, parent, tmp, field);                                                                                                                                   \
                    tmp = RB_RIGHT(parent, field);                                                                                                                                              \
                }                                                                                                                                                                               \
                if ((RB_LEFT(tmp, field) == NULL || RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) && (RB_RIGHT(tmp, field) == NULL || RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK)) { \
                    RB_COLOR(tmp, field) = RB_RED;                                                                                                                                              \
                    elm = parent;                                                                                                                                                               \
                    parent = RB_PARENT(elm, field);                                                                                                                                             \
                } else {                                                                                                                                                                        \
                    if (RB_RIGHT(tmp, field) == NULL || RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK) {                                                                                    \
                        struct type* oleft;                                                                                                                                                     \
                        if ((oleft = RB_LEFT(tmp, field))                                                                                                                                       \
                            != NULL)                                                                                                                                                            \
                            RB_COLOR(oleft, field) = RB_BLACK;                                                                                                                                  \
                        RB_COLOR(tmp, field) = RB_RED;                                                                                                                                          \
                        RB_ROTATE_RIGHT(head, tmp, oleft, field);                                                                                                                               \
                        tmp = RB_RIGHT(parent, field);                                                                                                                                          \
                    }                                                                                                                                                                           \
                    RB_COLOR(tmp, field) = RB_COLOR(parent, field);                                                                                                                             \
                    RB_COLOR(parent, field) = RB_BLACK;                                                                                                                                         \
                    if (RB_RIGHT(tmp, field))                                                                                                                                                   \
                        RB_COLOR(RB_RIGHT(tmp, field), field) = RB_BLACK;                                                                                                                       \
                    RB_ROTATE_LEFT(head, parent, tmp, field);                                                                                                                                   \
                    elm = RB_ROOT(head);                                                                                                                                                        \
                    break;                                                                                                                                                                      \
                }                                                                                                                                                                               \
            } else {                                                                                                                                                                            \
                tmp = RB_LEFT(parent, field);                                                                                                                                                   \
                if (RB_COLOR(tmp, field) == RB_RED) {                                                                                                                                           \
                    RB_SET_BLACKRED(tmp, parent, field);                                                                                                                                        \
                    RB_ROTATE_RIGHT(head, parent, tmp, field);                                                                                                                                  \
                    tmp = RB_LEFT(parent, field);                                                                                                                                               \
                }                                                                                                                                                                               \
                if ((RB_LEFT(tmp, field) == NULL || RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) && (RB_RIGHT(tmp, field) == NULL || RB_COLOR(RB_RIGHT(tmp, field), field) == RB_BLACK)) { \
                    RB_COLOR(tmp, field) = RB_RED;                                                                                                                                              \
                    elm = parent;                                                                                                                                                               \
                    parent = RB_PARENT(elm, field);                                                                                                                                             \
                } else {                                                                                                                                                                        \
                    if (RB_LEFT(tmp, field) == NULL || RB_COLOR(RB_LEFT(tmp, field), field) == RB_BLACK) {                                                                                      \
                        struct type* oright;                                                                                                                                                    \
                        if ((oright = RB_RIGHT(tmp, field))                                                                                                                                     \
                            != NULL)                                                                                                                                                            \
                            RB_COLOR(oright, field) = RB_BLACK;                                                                                                                                 \
                        RB_COLOR(tmp, field) = RB_RED;                                                                                                                                          \
                        RB_ROTATE_LEFT(head, tmp, oright, field);                                                                                                                               \
                        tmp = RB_LEFT(parent, field);                                                                                                                                           \
                    }                                                                                                                                                                           \
                    RB_COLOR(tmp, field) = RB_COLOR(parent, field);                                                                                                                             \
                    RB_COLOR(parent, field) = RB_BLACK;                                                                                                                                         \
                    if (RB_LEFT(tmp, field))                                                                                                                                                    \
                        RB_COLOR(RB_LEFT(tmp, field), field) = RB_BLACK;                                                                                                                        \
                    RB_ROTATE_RIGHT(head, parent, tmp, field);                                                                                                                                  \
                    elm = RB_ROOT(head);                                                                                                                                                        \
                    break;                                                                                                                                                                      \
                }                                                                                                                                                                               \
            }                                                                                                                                                                                   \
        }                                                                                                                                                                                       \
        if (elm)                                                                                                                                                                                \
            RB_COLOR(elm, field) = RB_BLACK;                                                                                                                                                    \
    }                                                                                                                                                                                           \
                                                                                                                                                                                                \
    attr struct type*                                                                                                                                                                           \
        name##_RB_REMOVE(struct name* head, struct type* elm)                                                                                                                                   \
    {                                                                                                                                                                                           \
        struct type *child, *parent, *old = elm;                                                                                                                                                \
        int color;                                                                                                                                                                              \
        if (RB_LEFT(elm, field) == NULL)                                                                                                                                                        \
            child = RB_RIGHT(elm, field);                                                                                                                                                       \
        else if (RB_RIGHT(elm, field) == NULL)                                                                                                                                                  \
            child = RB_LEFT(elm, field);                                                                                                                                                        \
        else {                                                                                                                                                                                  \
            struct type* left;                                                                                                                                                                  \
            elm = RB_RIGHT(elm, field);                                                                                                                                                         \
            while ((left = RB_LEFT(elm, field)) != NULL)                                                                                                                                        \
                elm = left;                                                                                                                                                                     \
            child = RB_RIGHT(elm, field);                                                                                                                                                       \
            parent = RB_PARENT(elm, field);                                                                                                                                                     \
            color = RB_COLOR(elm, field);                                                                                                                                                       \
            if (child)                                                                                                                                                                          \
                RB_PARENT(child, field) = parent;                                                                                                                                               \
            if (parent) {                                                                                                                                                                       \
                if (RB_LEFT(parent, field) == elm)                                                                                                                                              \
                    RB_LEFT(parent, field) = child;                                                                                                                                             \
                else                                                                                                                                                                            \
                    RB_RIGHT(parent, field) = child;                                                                                                                                            \
                RB_AUGMENT(parent);                                                                                                                                                             \
            } else                                                                                                                                                                              \
                RB_ROOT(head) = child;                                                                                                                                                          \
            if (RB_PARENT(elm, field) == old)                                                                                                                                                   \
                parent = elm;                                                                                                                                                                   \
            (elm)->field = (old)->field;                                                                                                                                                        \
            if (RB_PARENT(old, field)) {                                                                                                                                                        \
                if (RB_LEFT(RB_PARENT(old, field), field) == old)                                                                                                                               \
                    RB_LEFT(RB_PARENT(old, field), field) = elm;                                                                                                                                \
                else                                                                                                                                                                            \
                    RB_RIGHT(RB_PARENT(old, field), field) = elm;                                                                                                                               \
                RB_AUGMENT(RB_PARENT(old, field));                                                                                                                                              \
            } else                                                                                                                                                                              \
                RB_ROOT(head) = elm;                                                                                                                                                            \
            RB_PARENT(RB_LEFT(old, field), field) = elm;                                                                                                                                        \
            if (RB_RIGHT(old, field))                                                                                                                                                           \
                RB_PARENT(RB_RIGHT(old, field), field) = elm;                                                                                                                                   \
            if (parent) {                                                                                                                                                                       \
                left = parent;                                                                                                                                                                  \
                do {                                                                                                                                                                            \
                    RB_AUGMENT(left);                                                                                                                                                           \
                } while ((left = RB_PARENT(left, field)) != NULL);                                                                                                                              \
            }                                                                                                                                                                                   \
            goto color;                                                                                                                                                                         \
        }                                                                                                                                                                                       \
        parent = RB_PARENT(elm, field);                                                                                                                                                         \
        color = RB_COLOR(elm, field);                                                                                                                                                           \
        if (child)                                                                                                                                                                              \
            RB_PARENT(child, field) = parent;                                                                                                                                                   \
        if (parent) {                                                                                                                                                                           \
            if (RB_LEFT(parent, field) == elm)                                                                                                                                                  \
                RB_LEFT(parent, field) = child;                                                                                                                                                 \
            else                                                                                                                                                                                \
                RB_RIGHT(parent, field) = child;                                                                                                                                                \
            RB_AUGMENT(parent);                                                                                                                                                                 \
        } else                                                                                                                                                                                  \
            RB_ROOT(head) = child;                                                                                                                                                              \
    color:                                                                                                                                                                                      \
        if (color == RB_BLACK)                                                                                                                                                                  \
            name##_RB_REMOVE_COLOR(head, parent, child);                                                                                                                                        \
        return (old);                                                                                                                                                                           \
    }                                                                                                                                                                                           \
                                                                                                                                                                                                \
    /* Inserts a node into the RB tree */                                                                                                                                                       \
    attr struct type*                                                                                                                                                                           \
        name##_RB_INSERT(struct name* head, struct type* elm)                                                                                                                                   \
    {                                                                                                                                                                                           \
        struct type* tmp;                                                                                                                                                                       \
        struct type* parent = NULL;                                                                                                                                                             \
        int comp = 0;                                                                                                                                                                           \
        tmp = RB_ROOT(head);                                                                                                                                                                    \
        while (tmp) {                                                                                                                                                                           \
            parent = tmp;                                                                                                                                                                       \
            comp = (cmp)(elm, parent);                                                                                                                                                          \
            if (comp < 0)                                                                                                                                                                       \
                tmp = RB_LEFT(tmp, field);                                                                                                                                                      \
            else if (comp > 0)                                                                                                                                                                  \
                tmp = RB_RIGHT(tmp, field);                                                                                                                                                     \
            else                                                                                                                                                                                \
                return (tmp);                                                                                                                                                                   \
        }                                                                                                                                                                                       \
        RB_SET(elm, parent, field);                                                                                                                                                             \
        if (parent != NULL) {                                                                                                                                                                   \
            if (comp < 0)                                                                                                                                                                       \
                RB_LEFT(parent, field) = elm;                                                                                                                                                   \
            else                                                                                                                                                                                \
                RB_RIGHT(parent, field) = elm;                                                                                                                                                  \
            RB_AUGMENT(parent);                                                                                                                                                                 \
        } else                                                                                                                                                                                  \
            RB_ROOT(head) = elm;                                                                                                                                                                \
        name##_RB_INSERT_COLOR(head, elm);                                                                                                                                                      \
        return (NULL);                                                                                                                                                                          \
    }                                                                                                                                                                                           \
                                                                                                                                                                                                \
    /* Finds the node with the same key as elm */                                                                                                                                               \
    attr struct type*                                                                                                                                                                           \
        name##_RB_FIND(struct name* head, struct type* elm)                                                                                                                                     \
    {                                                                                                                                                                                           \
        struct type* tmp = RB_ROOT(head);                                                                                                                                                       \
        int comp;                                                                                                                                                                               \
        while (tmp) {                                                                                                                                                                           \
            comp = cmp(elm, tmp);                                                                                                                                                               \
            if (comp < 0)                                                                                                                                                                       \
                tmp = RB_LEFT(tmp, field);                                                                                                                                                      \
            else if (comp > 0)                                                                                                                                                                  \
                tmp = RB_RIGHT(tmp, field);                                                                                                                                                     \
            else                                                                                                                                                                                \
                return (tmp);                                                                                                                                                                   \
        }                                                                                                                                                                                       \
        return (NULL);                                                                                                                                                                          \
    }                                                                                                                                                                                           \
                                                                                                                                                                                                \
    /* Finds the first node greater than or equal to the search key */                                                                                                                          \
    attr struct type*                                                                                                                                                                           \
        name##_RB_NFIND(struct name* head, struct type* elm)                                                                                                                                    \
    {                                                                                                                                                                                           \
        struct type* tmp = RB_ROOT(head);                                                                                                                                                       \
        struct type* res = NULL;                                                                                                                                                                \
        int comp;                                                                                                                                                                               \
        while (tmp) {                                                                                                                                                                           \
            comp = cmp(elm, tmp);                                                                                                                                                               \
            if (comp < 0) {                                                                                                                                                                     \
                res = tmp;                                                                                                                                                                      \
                tmp = RB_LEFT(tmp, field);                                                                                                                                                      \
            } else if (comp > 0)                                                                                                                                                                \
                tmp = RB_RIGHT(tmp, field);                                                                                                                                                     \
            else                                                                                                                                                                                \
                return (tmp);                                                                                                                                                                   \
        }                                                                                                                                                                                       \
        return (res);                                                                                                                                                                           \
    }                                                                                                                                                                                           \
                                                                                                                                                                                                \
    /* ARGSUSED */                                                                                                                                                                              \
    attr struct type*                                                                                                                                                                           \
        name##_RB_NEXT(struct type* elm)                                                                                                                                                        \
    {                                                                                                                                                                                           \
        if (RB_RIGHT(elm, field)) {                                                                                                                                                             \
            elm = RB_RIGHT(elm, field);                                                                                                                                                         \
            while (RB_LEFT(elm, field))                                                                                                                                                         \
                elm = RB_LEFT(elm, field);                                                                                                                                                      \
        } else {                                                                                                                                                                                \
            if (RB_PARENT(elm, field) && (elm == RB_LEFT(RB_PARENT(elm, field), field)))                                                                                                        \
                elm = RB_PARENT(elm, field);                                                                                                                                                    \
            else {                                                                                                                                                                              \
                while (RB_PARENT(elm, field) && (elm == RB_RIGHT(RB_PARENT(elm, field), field)))                                                                                                \
                    elm = RB_PARENT(elm, field);                                                                                                                                                \
                elm = RB_PARENT(elm, field);                                                                                                                                                    \
            }                                                                                                                                                                                   \
        }                                                                                                                                                                                       \
        return (elm);                                                                                                                                                                           \
    }                                                                                                                                                                                           \
                                                                                                                                                                                                \
    /* ARGSUSED */                                                                                                                                                                              \
    attr struct type*                                                                                                                                                                           \
        name##_RB_PREV(struct type* elm)                                                                                                                                                        \
    {                                                                                                                                                                                           \
        if (RB_LEFT(elm, field)) {                                                                                                                                                              \
            elm = RB_LEFT(elm, field);                                                                                                                                                          \
            while (RB_RIGHT(elm, field))                                                                                                                                                        \
                elm = RB_RIGHT(elm, field);                                                                                                                                                     \
        } else {                                                                                                                                                                                \
            if (RB_PARENT(elm, field) && (elm == RB_RIGHT(RB_PARENT(elm, field), field)))                                                                                                       \
                elm = RB_PARENT(elm, field);                                                                                                                                                    \
            else {                                                                                                                                                                              \
                while (RB_PARENT(elm, field) && (elm == RB_LEFT(RB_PARENT(elm, field), field)))                                                                                                 \
                    elm = RB_PARENT(elm, field);                                                                                                                                                \
                elm = RB_PARENT(elm, field);                                                                                                                                                    \
            }                                                                                                                                                                                   \
        }                                                                                                                                                                                       \
        return (elm);                                                                                                                                                                           \
    }                                                                                                                                                                                           \
                                                                                                                                                                                                \
    attr struct type*                                                                                                                                                                           \
        name##_RB_MINMAX(struct name* head, int val)                                                                                                                                            \
    {                                                                                                                                                                                           \
        struct type* tmp = RB_ROOT(head);                                                                                                                                                       \
        struct type* parent = NULL;                                                                                                                                                             \
        while (tmp) {                                                                                                                                                                           \
            parent = tmp;                                                                                                                                                                       \
            if (val < 0)                                                                                                                                                                        \
                tmp = RB_LEFT(tmp, field);                                                                                                                                                      \
            else                                                                                                                                                                                \
                tmp = RB_RIGHT(tmp, field);                                                                                                                                                     \
        }                                                                                                                                                                                       \
        return (parent);                                                                                                                                                                        \
    }

#define RB_NEGINF -1
#define RB_INF 1

#define RB_INSERT(name, x, y) name##_RB_INSERT(x, y)
#define RB_REMOVE(name, x, y) name##_RB_REMOVE(x, y)
#define RB_FIND(name, x, y) name##_RB_FIND(x, y)
#define RB_NFIND(name, x, y) name##_RB_NFIND(x, y)
#define RB_NEXT(name, x, y) name##_RB_NEXT(y)
#define RB_PREV(name, x, y) name##_RB_PREV(y)
#define RB_MIN(name, x) name##_RB_MINMAX(x, RB_NEGINF)
#define RB_MAX(name, x) name##_RB_MINMAX(x, RB_INF)

#define RB_FOREACH(x, name, head)  \
    for ((x) = RB_MIN(name, head); \
         (x) != NULL;              \
         (x) = name##_RB_NEXT(x))

#define RB_FOREACH_FROM(x, name, y)                               \
    for ((x) = (y);                                               \
         ((x) != NULL) && ((y) = name##_RB_NEXT(x), (x) != NULL); \
         (x) = (y))

#define RB_FOREACH_SAFE(x, name, head, y)                         \
    for ((x) = RB_MIN(name, head);                                \
         ((x) != NULL) && ((y) = name##_RB_NEXT(x), (x) != NULL); \
         (x) = (y))

#define RB_FOREACH_REVERSE(x, name, head) \
    for ((x) = RB_MAX(name, head);        \
         (x) != NULL;                     \
         (x) = name##_RB_PREV(x))

#define RB_FOREACH_REVERSE_FROM(x, name, y)                       \
    for ((x) = (y);                                               \
         ((x) != NULL) && ((y) = name##_RB_PREV(x), (x) != NULL); \
         (x) = (y))

#define RB_FOREACH_REVERSE_SAFE(x, name, head, y)                 \
    for ((x) = RB_MAX(name, head);                                \
         ((x) != NULL) && ((y) = name##_RB_PREV(x), (x) != NULL); \
         (x) = (y))

#endif /* UV_TREE_H_ */
